Changes in Family Income and
Income Inequality Among Seniors in Canada
Tammy Schirle
Department of Economics, Wilfrid Laurier University
Preliminary Draft - please do not cite without permission
tschirle@wlu.ca
ABSTRACT
The distribution of family income among seniors in Canada has changed substantially over the past decade, reflecting an overall increase in family income and
an increase in income inequality. In this study, I use semi-parametric decomposition methods (developed by DInardo, Fortin and Lemieux, 1996) to determine
the extent to which various factors have contributed to this shift in the income
distribution. I focus on disentangling the efects of recent increases in elderly
labour market activity and the effect of changes in women’s experiences in the
labour force over the past four decades as this now translates into greater access
to pensions and other retirement income independent of their marital status. Using Canadian data from the Survey of Labour and Income Dynamics, I find that
increases in employment among elderly men and women can account for a large
portion of the change in equivalent after-tax family income inequality among senior families. Most notable, the results suggest inequality among senior families
would be substantially lower in 2004 if women’s access to pensions had remained
at its lower rates in 1996. Other important factors that help explain the changes
in income inequality include changes in women’s education and past experience
in the labour force, men’s education levels, and access to public pensions.
1.
Introduction
It has long been recognized that Canada’s retirement income programs have improved
the well being of many Canadian seniors. The Old Age Security pension, introduced in 1952
and expanded to those age 65 in 1965, coupled with the Guaranteed Income Supplement
(established in 1967) has brought up the incomes of the poorest seniors and reduced the
incidence of elderly poverty Milligan (Forthcoming).
Over the past decade, we’ve seen a substantial shift in the distribution of elderly incomes,
representing an overall increase in incomes. However, the increase in income has not been
experienced by all seniors resulting in higher income inequality among senior families. The
–2–
increases in income also appears to coincide with increases in the likelihood of employment
among seniors. As such, this shift may or may not reflect an improvement in senior families’
well-being.
The objective of this paper is to evaluate the extent to which various factors have caused
the recent shift in the income distribution. The focus is on how seniors’ incomes - the amount
and sources - have changed over the past decade and the relationship between those changes
and changes in the labour market activity of women, observed over the past 50 years.
I use Canadian data from the Survey of Labour and Income Dynamics (1996 & 2004
public use files) to examine changes in the equivalent after tax family income of census
families whose oldest member is age 65-79. I use the decomposition methods developed in
DiNardo et al. (1996) to examine how changes in the likelihood of older men and women
to be employed, men and women’s access to employer-provided pension income, access to
CPP/QPP benefits, and the structure of these income sources has affected the income distribution. I also investigate how changes in family composition (in part influenced by increases
in longevity), men’s and women’s education levels and labour market experience, have driven
changes in the income distribution.
I begin in the following section by briefly describing the data used in this study, the
measurement of incomes and key variable definitions. In section 3 I provide some background
for this study, describing the shift in the distribution of income and changes in various factors
that might influence the distribution of incomes. In section 4 I describe the methodology
used in the decompositions. Details of the implementation of this procedure are provided in
an appendix. Results are presented in section 5 followed by some concluding remarks and
discussion of next steps for this project.
2.
Data Sources
The primary data source for this project is the Survey of Labour and Income Dynamics,
focussing on the years 1996 and 2004.1 In this paper, I am only discussing after-tax income
(using Statistics Canada’s definition) as this best represents the income available for consumption among the available measures. This includes all market income (wages, pensions
and investment income) and government transfers (such as Old Age Security and Canada
Pension Plan benefits), but excludes items such as RRSP withdrawals.2
1
I am using the public use files and will start using the 2005 files as soon as possible. I have not yet
received RDC access for this project.
2
As a definition of after-tax income:
Market income includes earnings plus other market income, which comprises investment income, pension income, alimony income, and other taxable income. Total income is the sum of
–3–
I am interested in the incomes of census families in which the oldest member is between
the ages of 65 and 79. When sampling, I exclude any families in which key demographic
information is missing (age, education, and marital status). In this paper, I have chosen to
focus on the census family unit rather than the economic family unit, as I would like to relate
the results to the well-being of seniors. The census family will include single individuals or
married couples (including common-law couples) and their never-married children. In the
sample of interest here, a census family will typically be a married couple, a widow, or a
divorced individual. There are rarely never-married children still living with parents who
are over 65. An economic family, on the other hand, would include the older individuals
of interest and any relatives that are living in the same household. If it were the case, for
example, that individual seniors incomes declined dramatically such that they were forced
to live with their children, and we used the economic family unit to measure incomes, we
could see an increase in senior families’ incomes simply because they have moved into their
children’s homes.
I have also decided to sample according to the age of the oldest family member rather
than the more traditionally defined ‘head’ of the family based on the major income earner
because many income sources for seniors are based on the age of the oldest member. Further,
the major income earner in the family when they were younger may not necessarily be the
major income earner when elderly.
When discussing the income distribution of senior families, it is most appropriate to use
a measure of equivalent family income that accounts for the economies of scale that can be
achieved by a family and allows us to compare the incomes of single individuals to married
couples or larger families. In this paper, I rely on a commonly used measure of equivalent
family income, which divides the total family income by the square root of the number of
people in the family:
Y
Af ter − tax f amily income
= √
N umber of f amily members
(1)
As the vast majority of senior families considered here have either one or 2 members, this will
represent a single individual’s income or a married couple’s income divided by approximately
1.4.3
market income and government transfer income. Government transfer income includes income
from the Child Tax Benefit, Old Age Security and Guaranteed Income Supplement/Spousal
Allowance, Social Assistance and Provincial Income Supplements, Employment Insurance Benefits, Worker’s Compensation Benefits, Canada/Quebec Pension Plan Benefits, and the Goods
and Services Tax Credit. After-tax income is total income minus federal and provincial income
taxes paid. – Skuterud et al. (2004)
3
In earlier research, Fortin and Schirle (2006) have found that other commonly used measures of equivalent
–4–
A key problem with using SLID in this study is that any individuals over the age 69
are asked for only limited labour market information. As such, I will be using the presence
of earnings to indicate employment and the presence of pension income to indicate receipt
of employer-provided pension income. These are not perfect measures since, for example,
the pension income reported in SLID includes any income from a registered pension plan or
RRIF (registered retirement income fund). In some cases this will reflect RRSPs that have
been converted to RRIFs (now required by age 71) and survivor benefits from a spouse’s
pension. While this is may be appropriate for interpreting income as a measure of well-being,
the interpretation of such income as indicating labour market experience is limited.
3.
Background
The distribution of income among seniors tends to be much more narrow than the income
distribution among younger families. This is exemplified in Figure 1 where kernel density
estimates of the equivalent family after tax income distribution for three age groups in 2004
is plotted. The distribution of income among families whose oldest member is between age 55
and 59 is much wider than the distribution of incomes among families whose oldest member
is age 60 to 64. Comparing the 55 to 59 and 60 to 64 age groups, the inward shift from
the right tail of this distribution to the middle reflects the fact that as individuals enter
retirement, most pensions only replace a portion of income and retirement will typically
result in reduced or no earnings.4
The difference between the income distribution among families whose oldest member is
age 65-79 and those age 60-64 is substantial. Similar to the early retirees, some of the shift
inward at the right tail reflects a shift away from employment income to pension income.
The inward shift at the left tail is more dramatic and reflects the importance of Old Age
Security (OAS) pensions and Guaranteed Income Supplement (GIS) benefits which become
available to a family once the oldest member is over age 65. The provision of these benefits
is credited with reducing the incidence of poverty among seniors ? To note, the mode of
this distribution (age 65-79) occurs at an income of $18,214. As of June 2008, maximum
benefit entitlement from OAS and GIS for a single individual over age 65 was $13,636. For a
married couple (who are both over age 65), the maximum benefit entitlement in June 2008
is $22,104 (or $15,630 as equivalent family income). Families with income (other than OAS)
less than $20,112 in 2008 are eligible for at least some GIS assistance.5 This mode suggests,
family income that place different weights, for example, on children than adults, will result in different levels
of income but the same general trends in average incomes or distribution measures.
4
To note, Milligan and Schirle (Forthcoming) have shown that a very small portion of older individuals
(roughly 4% of 55-64 year olds) simultaneously receive wage and pension income.
5
Assuming both are over age 65.
–5–
Fig. 1.— Equivalent Family Incomes, by Age Group
Kernel density estimates shown here are based on a sample of census families whose
oldest member is in each age group.
then, that many elderly families rely quite heavily on these public pensions for income.
In fact, the vast majority of seniors report government transfers as their major source
of income. Reported in Table 1, more than 63% of individuals in senior families reported
government transfers as their major source of income in 2004. Private retirement pensions
were the other leading source of income, with 28% of seniors reporting this as their major
source of income. Other market income, from wages, self-employment and investments, were
rarely reported as the major source of income.
Myles (2000) has shown that over the 1980s, there was a general downward trend in
inequality among seniors, which can also be attributed in part to the availability. Over the
past decade, however, there has been a general increase in income inequality. The kernel
density estimates of log equivalent after tax family income among senior families in 1996 and
2004 is provided in Figure 2 with relevant descriptive statistics provided in Table 2.
Overall we see an improvement in incomes among senior families. However, we can
see that the 90th and 50th percentiles of income have increased much faster than the 10th
percentile. Overall, the changes between 1996 and 2004 represent a movement of seniors
from low incomes, being heavily reliant on OAS and GIS benefits toward higher and middle
incomes. With many seniors left behind, however, there has been on increase inequality.
–6–
Table 1. Major Income Sources - Individuals in Senior Families
Source
1996
No income
0.24
Wages and salaries
2.82
Self-employment incom 1.21
Government transfers
69.72
Investment income
6.17
Retirement pensions
18.87
Other income
0.97
2004
0.07
3.48
2.03
62.8
3.22
27.76
0.65
Note. — Source: SLID, based on a
sample of individuals in census families
whose oldest member is between the ages
of 65 and 79.
Table 2. Equivalent After Tax Family Income Among Seniors (2004 prices)
Year
1996
2004 % Change
Mean
24930 27846
Median
20778 24100
Mode
14913 16815
Log differences:
90-10
1.077
1.14
90-50
.678
.644
50-10
.399
.496
Gini
.269
.269
10.5
13.8
11.3
5.6
-5.2
19.6
-0.1
Note. — See text for description of sample.
–7–
Fig. 2.— Log Equivalent Family Incomes Among Seniors, 1996 and 2004.
Kernel density estimates are shown here based on a sample of census families whose
oldest member is age 65-79.
Measured using the log difference between the 90th and 10th percentiles, inequality increased
slightly. However, the 50-10 differential increased quite substantially - by almost 20% over
this period.
This study provides an interesting examples of how the choice of inequality measure is
important. Despite the obvious shift and widening of the income distribution in Figure 2,
the Gini coefficient (presented in Table 2) does not change. This is related to the Gini’s
sensitivity to the middle of the income distribution. Despite a widening of the bottom end
of the income distribution, there was some compression in the high end of the distribution
reflected in the decrease in the 90-50 differential. In what follows, I will focus on changes in
the 50-10 differential as this best represents the changes in the distribution of interest here.
What might explain the change in the income distribution? Several family characteristics considered in this paper are described in Table 3. Both men and women have become
more likely to be employed by 2004. Their annual earnings, however, are not as high. This
will in part reflect delayed retirement past ge 65 (part year work) and likely an increase in
part time work.6 Despite declines in defined benefit plan coverage among Canadians age
15-69 (Milligan and Schirle Forthcoming), RPP benefit receipt increased for senior families
over this period. Pension receipt increased most for women, from 36 to 48%. Women also
saw larger gains in the level of pension benefits. From public pensions, women also saw large
6
Unfortunately we can’t check this in SLID as individuals over age 65 are not asked hours worked.
–8–
Table 3. Characteristics of Senior Families
Women
Employed
Earnings
Pension Recipient
Pension
CPP/QPP Recipient
CPP/QPP Benefits
Age
Education:
8 yrs or less
Some HS
HS grad
Post-sec (any below BA)
University (B.A +)
Marital Status:
Married
Divorced
Widowed
Never married
Men
1996 2004 % Change 1996 2004
.12
.19
37.4
.19
.3
15929 12196
-30.6 16813 12019
.36
.48
25.2
.63
.7
9514 11644
18.3 16569 18459
.67
.79
15
.92
.94
4924 4965
.8 7128 6735
68.8
69
.4
70.3
70.9
0.36
0.20
0.16
0.24
0.04
.51
.08
.34
.08
0.27
0.19
0.19
0.29
0.06
All Families
.54
.11
.29
.06
-23.3
-5.8
15.5
20.9
47.0
0.38
0.19
0.12
0.21
0.09
0.29
0.17
0.15
0.28
0.11
% Change
35.8
-39.9
9.6
10.2
2.2
-5.8
.9
-22.8
-12.1
24.6
29.9
15.6
6
27
-17
-33
Note. — See text for sample description, which includes families whose oldest member is
age 65-79. Income levels are conditional on receipt.
–9–
gains in access to CPP/QPP. Benefit levels (conditional on receiving some benefits) did not
change substantially over time.
Education should also play an important role in explaining the changes in the income
distribution. Men and women have become more likely to have graduated high school and
obtain at least some post-secondary education. finally, we might expect that changes in
family structure will matter for the income distribution. Increases in life expectance have
resulted in fewer widows and more married couples. Interestingly, there are fewer nevermarried and more divorced individuals over the same period.
4.
4.1.
Methodology
Some Notation
The notation in this section is incredibly cumbersome. In later versions of this paper,
most of this section will be transferred to an appendix. In general, I have used capital letters
to refer to actual incomes and small caps to refer to the natural logarithm.
To begin, I would like introduce the notation for the definition of equivalent after tax
family income:
Yt =
(EtF + RP PtF + CP PtF + uFt + EtM + RP PtM + CP PtM + uM
t + υt )
√
Nt
(2)
where
EtF
RP PtF
CP PtF
uFt
EtM
RP PtM
CP PtM
uM
t
υt
Nt
Earnings of the female member at time t
Registered pension plan income of the female member at time t
Canada/Quebec pension plan income of the female member at time t
Other income (and taxes) of the female member at time t
Earnings of the male member at time t
Registered pension plan income of the male member at time t
Canada/Quebec pension plan income of the male member at time t
Other income (and taxes) of the male member at time t
Income of other census family members
Number of census family members
All incomes are measured annually, due to data limitations. The logarithm of equivalent
after tax family income is then
yt = ln(EtF + ... + υt ) − 0.5 ln(Nt )
(3)
The decomposition will make use of the structure of individuals’ income. For example,
the earnings observed at time t among women is described by the equation
EtF = exp(eFXtβt ) ∗ HtF = exp(XtF βtF E + Ft E ) ∗ HtF
(4)
– 10 –
where
eFXtβt
HtF
XtF
βtF E
Ft E
Natural logarithm of hourly earnings
Annual hours worked
Female member’s characteristics at time t
Population parameters describing the structure of female earnings at time t
Residual female earnings at time t not explained by their characteristics.
The characteristics accounted for here include the individual’s highest level of education,
their experience in the paid employment, province of residence, age, and marital status (also
referred to as family composition, Ct )
Of course, not all individuals will have positive incomes from each source. The decomposition will explicitly account for this. Denote the presence of positive earnings for the
female member at time t as P EtF = 1 and zero earnings by P EtF = 0.
4.2.
Decomposing the distribution of income
The methodology used in this paper follows the work of DiNardo et al. (1996) and Fortin
and Schirle (2006). I outline the densities and counterfactual densities below, showing the
derivation of some equations in the appendix.
The density of log equivalent after tax family income at one point in time, ft (y), can be
written as the integral of the density of income conditional on a set of family characteristics
and given the structure of male and female income at date t:
Z
Z
ft (y) =
... f (y|P E F , P RF , P CP P F , P E M , P RM , P CP P M , C, X F , X M ;
βtF E , βtF R , βtF C , βtM E , βtM R , βtM C )
dF (P E F |P RF , P CP P F , P E M , P RM , P CP P M , C, X F , X M , tP E F |(·) = t)
dF (P RF |P CP P F , P E M , P RM , P CP P M , C, X F , X M , tP RF |(·) = t)
dF (P CP P F |P E M , P RM , P CP P M , C, X F , X M , tP CP P F |(·) = t)
dF (P E M |P RM , P CP P M , C, X F , X M , tP E M |(·) = t)
dF (P RM |P CP P M , C, X F , X M , tP P M |(·) = t)
dF (P CP P M |C, X F , X M , tP CP P M |(·) = t)
dF (C|X F , X M , tC|(·) = t)
dF (X F |X M , tX F |(·) = t)
dF (X M |tX M = t)
(5)
The decomposition involves the creation of counterfactual densities. Intuitively, each
stage of the decomposition takes the density of income in t=2004 and creates a new density
– 11 –
that would have prevailed had the family characteristic had not changed after s=1996, but
the other attributes not yet accounted for had changed.
In the first stage of the decomposition, I create a counterfactual density representing
the density of log equivalent after tax family income that would have prevailed had women’s
likelihood of being employed in the year (P E F ) not changed after 1996. This counterfactual
density would be represented by:
Z Z
fc1 (y) =
f (y|(·); βt ) dF (P E F |(·), tP E F |(·) = s)
dF (P RF , P CP P F , P E M , P RM , P CP P M , C, X F , X M |t(·) = t)
(6)
with obvious simplifications made to the notation here. This counterfactual can be obtained
from the original density by making use of a reweighting function:
Z Z
fc1 (y) =
f (y|(·); βt ) ψP E F |(·) dF (P E F |(·), tP E F |(·) = t)
where ψP E F |(·)
dF (P RF , P CP P F , P E M , P RM , P CP P M , C, X F , X M |t(·) = t) (7)
dF (P E F |(·), tP E F |(·) = s)
=
(8)
dF (P E F |(·), tP E F |(·) = t)
The presence of earnings (representing being employed) takes on values of 0 or 1. Hence,
the reweighting function (8) can be stated as
ψP E F |(·) = P E F
P r(P E F = 1|(·), tP E F |(·) = s)
P r(P E F = 1|(·), tP E F |(·) = t)
+(1 − P E F )
P r(P E F = 0|(·), tP E F |(·) = s)
P r(P E F = 0|(·), tP E F |(·) = t)
(9)
To obtain estimates of the above probabilities, I use a probit model in which the latent
variable describing a woman’s employment decision is a function of her age, education,
province of residence, marital status, previous full time full year experience in employment,
and whether the woman also has pension and CPP/QPP income. The predicted reweighting
function is then multiplied by the weights of each observation in the sample for which a female
head is present.
In the second stage of the decomposition, I adjust the density of income for changes in the
structure of women’s employment income (βtF E ). That is, I want to create the counterfactual
density
Z Z
fc2 (y) =
f (y|(·); βsF E , βtnotF E ) ψP E F |(·) dF (P E F |(·), tP E F |(·) = t)
dF (P P F , P CP P F , P E M , P P M , P CP P M , C, X F , X M |t(·) = t)
(10)
To do this, I first estimate women’s log hourly earnings in each year 1996 and 2004
and eFXsβs ) using a simple econometric model:
(eFXtβt
eFXtβt = XtF βtF E + Ft E
(11)
– 12 –
where XtF is a vector of characteristics specific to the female head of the census family.
This includes age, education, province of residence, marital status, and previous full time
full year experience in employment. Women’s earnings are then adjusted for changes in the
structure of earnings by applying the time s = 1996 parameter estimates βsF E to the time t
characteristics and adding the residuals of the time t = 2004 earnings regression. That is:
eFXtβs = XtF βsF E + Ft E .
(12)
These estimates are then used to adjust the equivalent family incomes of all families with a
female head (who had positive earnings) present.
The next few stages are similar in nature. In the third and fifth stages of the decomposition, I adjust the density of income for changes in the likelihood of women to have private
pension income (P RF ) and CPP/QPP benefits (P CP P F ) respectively using reweighting
functions similar to (8). In the fourth and sixth stages, I adjust the density of income for
changes in the structure of women’s private pensions and CPP/QPP benefits respectively.
At the sixth stage of the decomposition we have the counterfactual density:
Z Z
fc6 (y) =
M (·)
f (y|(·); βsF E , βsF R , βsF C βt
)
ψP E F |(·) dF (P E F |(·), tP E F |(·) = t)
ψP RF |(·) dF (P RF |P CP P F , P E M , P P M , P CP P M , C, X F , X M , tP RF |(·) = t)
ψP C F |(·) dF (P CP P F |P E M , P P M , P CP P M , C, X F , X M , tP C F |(·) = t)
dF (P E M , P P M , P CP P M , C, X F , X M , t(·) = t)
(13)
where
ψP RF |(·)
P r(P RF = 1|(·), tP RF |(·) = s)
= PR
P r(P RF = 1|(·), tP RF |(·) = t)
F
P r(P RF = 0|(·), tP RF |(·) = s)
+(1 − P R )
P r(P RF = 0|(·), tP RF |(·) = t)
F
(14)
and
ψP C F |(·) = P C F
P r(P C F = 1|(·), tP C F |(·) = s)
P r(P C F = 1|(·), tP C F |(·) = t)
+(1 − P C F )
P r(P C F = 0|(·), tP C F |(·) = s)
.
P r(P C F = 0|(·), tP C F |(·) = t)
(15)
The likelihood of receiving a pension is estimated using a probit in which the receipt of income
from a registered pension plan is a function of age, education, province, marital status,
previous full time full year experience and receipt of CPP/QPP benefits. The structure of
– 13 –
pension and CPP income uses the same model as in (11), where the dependent variable
is measured annually. The likelihood of receiving CPP/QPP benefits is estimated using
non-parametric techniques.7
These steps are then repeated to account for changes in men’s income and income
sources. In the seventh through twelfth stages, I adjust the density of income for changes
in the likelihood of men to have positive earnings, the structure of earnings, the likelihood
of having private pension income, the structure of pension income, the likelihood of having CPP/QPP benefits, and the structure of those benefits. At the twelfth stage of the
decomposition, we have the counterfactual density:
Z
fc12 (y) =
Z
...
f (y|(·); βsF E , βsF R , βsF C , βsM E , βsM R , βsM C )
ψP E F |(·) dF (P E F |(·), tP E F |(·) = t) ψP RF |(·) dF (P RF |(·), tP RF |(·) = t)
ψP C F |(·) dF (P CP P F |(·), tP CP P F |(·) = t)
ψP E M |(·) dF (P E M |(·), tP E M |(·) = t) ψP RM |(·) dF (P RM |(·), tP P M |(·) = t)
ψP C M |(·) dF (P CP P M |(·), tP CP P M |(·) = t)
dF (C, X F , X M , tC,X F ,X M = t)
(16)
The last three stages of the decomposition account for changes in family and individual
characteristics. In the thirteenth stage, I adjust the density of income for changes in family
structure. Families fall into four categories - (i) married or common-law, (ii) divorced or
separated, (iii) widowed, and (iv) never married. The following reweighting function is used
in the creation of the counterfactual density of income:
ψC|X
dF (C|X F , X M , tC|X = s)
=
dF (C|X F , X M , tC|X = t)
4
X
P r(C = j|X F , X M , tC|X = s)
=
Ij
P r(C = j|X F , X M , tC|X = t)
j=1
(17)
(18)
The probabilities used to estimate (18) are found using a multinomial logit model that
includes the age of the oldest family member (as a set of indicator variables) and province
of residence as covariates.
7
I find the cell-specific probabilities of having positive CPP/QPP income. For those with positive FTFY
experience, I create 3 age groups (under 64, 65-70 and 71+), married or single, in 2 education groups (High
school or less and more than high school). For those with zero FTFY experience, I use 3 age groups. Finally,
there are some with unknown experience that I break into the 3 age groups. In each cell, I find a simple
weighted mean to use as the probability.
– 14 –
In the fourteenth stage, the density of income is adjusted for changes in women’s characteristics (X F ). In families represented by a married or common law couples (such that a
male head is present), the reweighting function
ψX F |X M
dF (X F |X M , tX F |X M = s)
=
dF (X F |X M , tX F |X M = t)
(19)
P r(tX F |X M = s|X M , X F ) P r(tX F |X M = t|X M )
=
P r(tX F |X M = t|X M , X F ) P r(tX F |X M = s|X M )
(20)
is used to create the counterfactual density of income (see the appendix for its derivation).
To obtain estimates of the conditional probabilities, the samples from each year s and t
are pooled to estimate probit model with the year as the binary dependent variable. The
characteristics (X F , X M ) include education, age, years of full time full year experience and
province of residence.
For unmarried women (divorced, widowed, or never married), the reweighting function
simplifies to:
ψX F |X M =
P r(tX F = s|X F ) P r(tX F = t)
.
P r(tX F = t|X F ) P r(tX F = s)
(21)
Estimates of the conditional probabilities are again found using a probit model. The unconditional probabilities (P r(tX F = t)) are simply the weighted shares of each year’s sample in
the pooled sample.
The last stage of the decomposition accounts for the changes in men’s characteristics.
Here, the reweighting function
ψX M =
P r(tX M = s|X M ) P r(tX M = t)
.
P r(tX M = t|X M ) P r(tX M = s)
(22)
is applied to weights of all families with a male present. The conditional probabilities are
also again found using a simple probit model. At this final stage of the decomposition, we
have the counterfactual density
Z
Z
fc15 (y) =
... f (y|(·); βsF E , βsF R , βsF C , βsM E , βsM R , βsM C )
ψP E F |(·) dF (P E F |(·), tP E F |(·) = t) ψP RF |(·) dF (P RF |(·), tP RF |(·) = t)
ψP C F |(·) dF (P CP P F |(·), tP CP P F |(·) = t)
ψP E M |(·) dF (P E M |(·), tP E M |(·) = t) ψP RM |(·) dF (P RM |(·), tP P M |(·) = t)
ψP C M |(·) dF (P CP P M |(·), tP CP P M |(·) = t)
ψC|X dF (C|X F , X M , tC|X F ,X M = t) ψX F |X M dF (X F |X M , tX F |X M = t)
ψX M dF (X M |tX M = t)
(23)
– 15 –
This density represents what the time t density of log equivalent family after-tax income
would look like had each of the characteristics discussed here not changed since time s.
5.
Results
The decomposition begins with the role of changes in women’s employment. Presented
in Figure 3, we can see that if women had not increased their tendency to be employed over
time, more families would have remained at lower income levels (around the mode of the
distribution). The resulting shift toward lower incomes results in a large decrease in the
50-10 differential (see Table B).8 Changes in the structure of earnings had little effect. Note
that the estimates used in the creation of these counterfactuals are available in the appendix.
Income inequality may have been substantially lower had women’s access to pensions
remained as it was in 1996. Similar to their tendency to be employed, this lack of access
would have resulted in many of the families observed in 2004 (that had high incomes) to
be left in the lower income groups. The increased benefits for women are also an important
factor here. Again, Incomes would be lower if private pension benefits looked like they did
in 1996.
Women’s access to public pension (see Figure 5) also plays an important role in explaining the changes in the income distribution. If it were the case that women’s access to
CPP/QPP remained as it was in 1996, we would have observed higher income inequality
as the lower income women would not be receiving these benefits. Interestingly, changes
to the structure of CPP benefits have a visible effect on the income distribution but result
in few changes in inequality measures. While changes in CPP structure move the mode of
the distribution slightly, there are no other real changes in the distribution associated with
changes in CPP benefit structure.
Turning to men’s income sources (Figure 6), income inequality among seniors would
have been lower had men’s employment rates looked like they did in 1996. However, the
impact is not nearly as large as the impact of changes in women’s employment. Further,
there were no major changes in the income distribution that could be attributed to changes
in the structure of earnings.
Men’s access to pension (figure 7) does not appear to have had a substantial effect on
the income distribution. Similar to women’s access to pensions, if access had not increased
many families would have been left in lower income groups. The impact is visibly less than
women’s access to pensions, and there is little if any impact on measured inequality. Changes
8
The result appears exaggerated but I have not found a problem in the program. I continue to investigate
this.
– 16 –
Fig. 3.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 17 –
Fig. 4.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 18 –
Fig. 5.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 19 –
Fig. 6.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 20 –
to the structure of men’s pensions also has little effect. Changes in men’s CPP, which are
very small over this period, have had very little effect on the distribution of income (see
Figure 8).
In the top of Figure 9, the counterfactual density that would have prevailed had family
composition not changed since 1996 is presented. I found it surprising that despite large
reductions in the likelihood of being a widow over time, that such changes have not had a
substantial effect on the income distribution.
Changes in women’s and men’s characteristics, on the other hand, have had a significant
impact. If women had not become more educated and more experienced in the labour market,
we would have seen a much higher level of income inequality as many families would be taken
out of the middle of the income distribution and redistributed to the lowest income levels
(see Figure 9). Changes to men’s characteristics had the opposite large effect. If they had
remained less educated (as experience had not changed substantially over time for them),
many of these families would be redistributed from the higher income groups to middle
income groups, resulting in lower inequality.
– 21 –
Fig. 7.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 22 –
Fig. 8.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 23 –
Fig. 9.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 24 –
Fig. 10.— Counterfactual Densities of Log Equivalent After Tax Family Income (Primary
Decomposition Results)
– 25 –
Table 4. Inequality Statistics - Primary Order Decomposition
Density
90-10
90-50
50-10
Gini
1996
2004
Total Change
Counterfactual 2004 Densities
C.1 Women’s employment
1.077
1.14
0.063
0.678
0.644
-0.034
0.398
0.496
0.098
0.269
0.269
0
1.069
-(0.071)
1.074
(0.005)
1.07
-(0.004)
1.031
-(0.039)
1.044
(0.013)
1.05
(0.006)
1.029
-(0.021)
1.041
(0.012)
1.044
(0.003)
1.037
-(0.007)
1.052
(0.015)
1.049
-(0.003)
1.056
(0.007)
1.085
(0.029)
0.999
-(0.086)
0.641
-(0.003)
0.645
(0.004)
0.663
(0.018)
0.64
-(0.023)
0.648
(0.008)
0.656
(0.008)
0.647
-(0.009)
0.658
(0.011)
0.67
(0.012)
0.661
-(0.009)
0.662
(0.001)
0.657
-(0.005)
0.662
(0.005)
0.663
(0.001)
0.652
-(0.011)
0.428
-(0.068)
0.428
(0.000)
0.408
-(0.020)
0.391
-(0.017)
0.396
(0.005)
0.394
-(0.002)
0.382
-(0.012)
0.383
(0.001)
0.374
-(0.009)
0.377
(0.003)
0.39
(0.013)
0.392
(0.002)
0.394
(0.002)
0.422
(0.028)
0.347
-(0.075)
0.258
-(0.011)
0.26
(0.002)
0.262
(0.002)
0.252
-(0.010)
0.257
(0.005)
0.259
(0.002)
0.255
-(0.004)
0.269
(0.014)
0.275
(0.006)
0.272
-(0.003)
0.273
(0.001)
0.272
-(0.001)
0.275
(0.003)
0.282
(0.007)
0.261
-(0.021)
C.2 Structure of earnings
C.3 Women’s Pension access
C.4 Structure of pensions
C.5 Women’s CPP access
C.6 Structure of benefits
C.7 Men’s employment
C.8 Structure of earnings
C.9 Men’s Pension access
C.10 Structure of pensions
C.11 Men’s CPP access
C.12 Structure of benefits
C.13 Family Structure
C.14 Women’s characteristics
C.15 Men’s characteristics
Note. — In parentheses is the difference in inequality statistics between
each stage of the decomposition.
– 26 –
6.
Next Steps
The results of this study clearly show that changes in women’s income - the sources and
the amounts - are an important factor in explaining recent changes in the income distribution
of senior families. Women’s access to employer-provided pensions and their gains in pension
benefit levels are key factors for improving the well-being of senior families.
These results are preliminary and require further scrutiny. The next steps for this study
include
• changing the order of the decomposition,
• repeating the decomposition for before-tax incomes,
• truncating the sample to exclude the oldest individuals,
• and investigating the value of jointly estimating the receipt of income sources when
creating the counterfactual densities.
REFERENCES
DiNardo, John, Nicole M. Fortin, and Thomas Lemieux (1996) ‘Labor market institutions
and the distribution of wages, 1973-1992: A semiparametric approach.’ Econometrica
64(5), 1001–44
Fortin, Nicole M., and Tammy D. Schirle (2006) ‘Gender dimensions of changes in earnings
inequality in canada.’ In Dimensions of Inequality in Canada, ed. David A. Green
and Jonathan R. Kesselman (UBC Press: Vancouver) pp. 307–346
Milligan, Kevin (Forthcoming) ‘The evolution of elderly poverty in canada.’ Canadian Public
Policy
Milligan, Kevin, and Tammy Schirle (Forthcoming) ‘Working while receiving a pension:
Will double dipping change the elderly labour market?’ In Retirement policy issues
in Canada, Conference Proceedings, ed. Charles Beach (John Deutsch Institute)
Myles, John (2000) ‘The maturation of Canada’s retirement income system: Income levels,
income inequality and low-income among the elderly.’ Statistics Canada, Catalogue
no. 11F0019MPE No. 147
Skuterud, Mikal, Marc Frenette, and Preston Poon (2004) ‘Describing the distribution of income: Guidelines for effective analysis.’ Statistic Canada, Income Statistics Division,
Income Research Paper Series
– 27 –
A.
Derivation of reweighting functions
Equation 20:
ψX F |X M =
dF (X F |X M , tX F |X M = s)
dF (X F |X M , tX F |X M = t)
(A1)
(A2)
Using Bayes’ Rule for the numerator:
P r(X F |X M , tX F |X M = s)
=
P r(X M , tX F |X M = s|X F ) · P r(X F )
P r(X M , tX F |X M = s)
(A3)
=
P r(tX F |X M = s|X M , X F )P r(X M |X F )P r(X F )
P r(tX F |X M = s|X M )P r(X M )
(A4)
Placing this into the reweighting function and canceling terms :
M
F
P r(tX F |X M =s|X
ψX F |X M =
,X )
P r(tX F |X M =s|X M )
P r(t
X F |X M
=t|X M ,X F )
P r(tX F |X M =t|X M )
B.
Estimates used in the decomposition
This preprint was prepared with the AAS LATEX macros v5.2.
(A5)
– 28 –
Table 5. Women’s Income Sources: Probit coefficients
hfpen
hfcpp
rfeduc1
rfeduc2
rfeduc4
rfeduc5
hfagelt60
hfage6064
dhfage2
dhfage3
dhfage4
dhfage5
dhfage6
dhfage7
dhfage8
dhfage9
dhfage10
dhfage11
dhfage12
dhfage13
dhfage14
dhfage15
hfyrx0
hfyrx97
hfyrx1020
hfyrx2030
hfyrx3040
hfyrx4050
marstat2
marstat3
marstat4
prov1
prov2
prov3
prov4
prov6
prov7
prov8
prov9
prov10
cons
Employed 1996
Employed 2004
Pension 1996
Pension 2004
-0.257*
0.031
-0.555***
-0.285*
-0.078
0.361*
1.000***
0.496***
0.02
0.108
-0.174
-0.279
-0.346
-0.339
-0.608**
-1.163***
-0.614*
-0.722**
-1.402***
-0.938***
-0.893***
-0.969***
-0.039
0.552***
0.319*
0.607***
0.605***
0.687***
0.181
-0.094
-0.122
-0.301
0.334
-0.253
-0.172
0.135
0.315*
0.543***
0.23
0.195
-1.383***
0.053
-0.204*
-0.088
0.007
0.181
0.479***
0.556**
0.063
-0.204
-0.596***
-0.428**
-0.661***
-0.656***
-0.553**
-0.569**
-0.536**
-1.010***
-0.570**
-0.975***
-0.693**
-1.034***
-1.020***
-0.144
0.724***
0.284*
0.544***
0.629***
0.859***
0.269*
0.008
-0.128
-0.641**
-0.177
-0.439***
-0.148
-0.07
0.2
0.2
0.119
0.071
-0.908***
0.711***
-0.450***
-0.253*
0.146
0.504**
-1.155***
-0.616***
-0.129
0.021
-0.351*
-0.094
-0.047
0.202
0.197
0.184
0.370*
0.131
0.172
0.033
-0.012
-0.164
-0.256*
0.17
0.145
0.361**
0.300**
0.174
0.166
0.295***
0.666***
-0.437**
-0.158
-0.274*
0.036
0.17
0.231
0.045
0.026
0.183
-1.010***
0.802***
-0.506***
-0.285**
0.082
0.315*
-0.650**
-0.576***
-0.254
0.172
0.198
-0.061
0.601***
0.545***
0.445**
0.524***
0.714***
0.769***
0.535**
0.583***
0.498**
0.192
0.033
0.089
0.184
0.516***
0.737***
0.286*
-0.034
0.192**
0.212
-0.381**
-0.216
-0.104
-0.175
0.052
0.125
0.306**
-0.093
-0.043
-1.052***
Note. — egend: * p¡0.05; ** p¡0.01; *** p¡0.001
– 29 –
Table 6. Women’s Income Structure: OLS coefficients
rfeduc1
rfeduc2
rfeduc4
rfeduc5
hfagelt60
hfage6064
dhfage2
dhfage3
dhfage4
dhfage5
hfyrx0
hfyrx97
hfyrx1020
hfyrx2030
hfyrx3040
hfyrx4050
marstat2
marstat3
marstat4
prov1
prov2
prov3
prov4
prov6
prov7
prov8
prov9
prov10
dhfage6
dhfage7
dhfage8
dhfage9
dhfage10
dhfage11
dhfage12
dhfage13
dhfage14
dhfage15
cons
Earnings 1996
Earnings 2004
Pension 1996
Pension 2004
CPP 2004
-0.334
-0.293
-0.095
0.007
-0.213
-0.165
-0.408
-0.312
0.235
-0.173
0.122
-0.343
0.033
-0.11
-0.062
0.02
-0.233
-0.048
0.333
1.121
-0.878
0.681
0.297
0.552**
0.14
0.354
0.627*
0.431
0.098
-0.184
0.09
0.224
-0.054
0.202
-0.085
-0.034
-0.016
-0.019
0.201
0.005
-0.08
0.092
-0.395
-0.073
0.186
0.446
0.459
-0.18
0.174
-0.134
-0.104
0.01
0.14
-0.172
0.078
0.262
2.613***
2.477***
-0.373***
-0.149
0.179*
0.882***
0.61
0.623***
-0.193
0.377**
0.08
0.143
0.366**
0.027
-0.076
0.318**
0.230*
0.211*
0.22
0.500***
0.675***
0.095
0.476
0.154
0.142
0.224**
0.087
0.073
0.216
0.365***
0.204
0.067
0.142
-0.16
-0.216
0.131
0.097
0.013
-0.101
0.007
7.933***
-0.616***
-0.431***
-0.019
0.883***
0.698*
0.453***
0.04
0.044
0.194
-0.053
0.187
0.139
0.114
0.308***
0.556***
0.216*
0.358***
0.670***
1.123***
0.234
0.38
0.256
0.303
0.386***
0.111
0.118
0.081
0.479***
-0.17
0.143
0.079
0.018
0.067
0.097
-0.433***
0.064
-0.125
0.268
8.012***
-0.305***
-0.218***
-0.004
0.281***
0.818***
0.159
0.022
0.02
0.09
0.155
-0.044
0.401***
0.383***
0.654***
0.575***
0.731***
0.205***
0.789***
0.396***
-0.429**
-0.076
0.043
0.027
0.057
0.023
0.004
-0.077
0.07
-0.193*
0.099
-0.047
-0.003
0.098
-0.041
-0.001
0.093
0.086
0.11
7.492***
Note. — egend: * p¡0.05; ** p¡0.01; *** p¡0.001
– 30 –
Table 7. Men’s Income Sources: Probit coefficients
hmpen
hmcpp
rmeduc1
rmeduc2
rmeduc4
rmeduc5
hmagelt60
hmage6064
dhmage2
dhmage3
dhmage4
dhmage5
dhmage6
dhmage7
dhmage8
dhmage9
dhmage10
dhmage11
dhmage12
dhmage13
dhmage14
dhmage15
hmyrx0
hmyrx97
hmyrx1020
hmyrx2030
hmyrx3040
hmyrx4050
marstat2
marstat3
marstat4
prov1
prov2
prov3
prov4
prov6
prov7
prov8
prov9
prov10
cons
Employed 1996
Employed 2004
Pension 1996
Pension 2004
-0.276***
-0.085
-0.107
-0.09
0.079
0.580***
0.918*
0.565*
-0.068
-0.164
-0.410*
-0.665***
-0.581***
-0.621***
-0.730***
-0.594**
-0.794***
-0.783***
-0.975***
-0.833***
-0.992***
-1.497***
-0.148
0.718*
0.241
0.039
0.267
0.840**
-0.382*
-0.188
0.044
-0.31
0.486**
-0.136
-0.046
0.206
0.356*
0.828***
0.347*
0.052
-1.027**
0.081
-0.174
-0.299**
-0.158
-0.007
-0.035
0.989*
0.493*
0.063
-0.215
-0.223
-0.490**
-0.531***
-0.675***
-0.446**
-0.503**
-0.774***
-0.681***
-0.566***
-0.893***
-0.752***
-1.158***
-0.952**
0.154
-0.395
-0.454
-0.143
0.124
-0.189
-0.254*
-0.152
-0.606***
0.018
-0.407**
-0.237
0.037
0.126
0.225
0.113
-0.141
0.14
1.466***
-0.457***
-0.066
0.203
0.418*
0.501
-0.678**
0.134
-0.002
-0.147
-0.048
0.076
-0.017
0.246
0.074
0.261
0.368*
0.187
0.416*
0.131
-0.114
-0.437
0.228
-0.004
-0.126
0.287
0.406
-0.343*
0.044
-0.545***
-0.410**
-0.615***
-0.387**
-0.158
-0.055
-0.172
-0.236
-0.304*
-0.127
-1.103***
1.564***
-0.328**
-0.099
0.097
0.435**
0.107
-0.441*
-0.161
-0.055
-0.104
0.023
0.298
0.447**
0.197
0.417*
0.272
0.448**
0.195
0.491**
0.368*
0.518*
0.469
0.427
0.209
0.718**
1.043***
0.757**
-0.376**
0.002
-0.313
-0.600***
-0.269
-0.084
-0.059
0.171
-0.051
-0.001
-0.003
0.023
-1.770***
Note. — egend: * p¡0.05; ** p¡0.01; *** p¡0.001
– 31 –
Table 8. Men’s Income Structure: OLS coefficients
rmeduc1
rmeduc2
rmeduc4
rmeduc5
hmagelt60
hmage6064
dhmage2
dhmage3
dhmage4
dhmage5
hmyrx0
hmyrx97
hmyrx1020
hmyrx2030
hmyrx3040
hmyrx4050
marstat2
marstat3
marstat4
prov1
prov2
prov3
prov4
prov6
prov7
prov8
prov9
prov10
dhmage6
dhmage7
dhmage8
dhmage9
dhmage10
dhmage11
dhmage12
dhmage13
dhmage14
dhmage15
cons
Earnings 1996
Earnings 2004
Pension 1996
Pension 2004
CPP 2004
-0.623
-1.278***
-0.926**
-0.557
-0.154
-0.759*
0.443
0.039
-0.492
-0.057
0
-0.374
-0.404
0.898
0.091
-0.012
0.254
-1.245
0.195
-0.429
0.031
0.254
0.147
0.424
-0.552
0.558
-1.095**
0.615
-0.299
-0.284
-0.339
0.239
0.391
0.385
0.268
0.457
-0.263
0.128
2.55
0.306
1.328
-0.068
-0.391
0.181
0.253
-0.271
-1.299**
-0.658
-0.511
0
-0.413
-0.069
-0.57
-0.054
-0.159
-0.365
3.385***
2.503*
-0.688***
-0.059
0.062
0.616***
0.209
0.279
-0.147
-0.230*
-0.282*
-0.016
0.562
0.176
0.153
-0.107
0.296
0.086
-0.252*
0.007
-0.202
-0.123
-0.138
0.072
0.049
0.167**
-0.073
-0.095
0.006
-0.009
-0.167
-0.352**
-0.077
-0.1
-0.1
-0.181
0.036
-0.075
-0.278
-0.136
9.280***
-0.759***
-0.439***
0.011
0.760***
-0.262
-0.29
-0.357**
-0.169
-0.444***
-0.537***
-0.33
-0.336
-0.649*
-0.371
0.146
-0.161
-0.1
0.108
0.033
0.069
0.154
0.146
0.272
0.303***
0.378**
0.06
0.095
0.194*
-0.473***
-0.447***
0.069
-0.294*
-0.340**
-0.165
-0.231
-0.261*
-0.465***
-0.253
9.613***
-0.012
0.049
0.157***
0.268***
-0.487
-0.264**
0.061
-0.014
-0.065
0.049
0.159
0.116
0.093
0.092
0.230**
0.337***
-0.025
0.063
-0.351***
-0.052
-0.062
0.014
-0.098
0.032
0.097
-0.032
-0.224***
-0.072
-0.089
0.02
0.05
-0.064
-0.021
-0.075
0.041
0.063
0.002
-0.001
8.369***
Note. — egend: * p¡0.05; ** p¡0.01; *** p¡0.001